Intermediate Algebra Extended Final Exam Review Questions
1. a) Graph the equation
b) What is the x-intercept?
c) What is the y-intercept?
d) What is the slope of this line ?
2. a) Find the slope of the line joining the points and .
b) Find the equation of this line.
3. The equations and represent two lines that are
4. Find the equation of the line through the point with .
5. Find the slope and y- intercept of the line .
6. Find the equation of the line through the point, and
b) perpendicular , to the line .
7. Graph the solution set of .
8. Simplify . Write all solutions using only positive
9. Write in simplest radical form . Assume all variables are positive.
10. Write in simplest radical form. Assume all variables are positive .
11. Write in simplest form using rational exponents .
12. Simplify. Assume all variables are positive real numbers.
15. Perform the indicated operation .
16. Solve each equation.
17. Use the discriminant to discuss the nature of the
roots of .
19. The graph of is a
a) What is the equation of its axis of symmetry?
b) Is its vertex a maximum or a minimum point?
c) What are the coordinates of its vertex?
d) What is the y-intercept of the graph?
e) What, if any, are the x-intercepts of the graph?
20. Solve for x:
21. Define each of the following:
a) 2 linear equations are dependent
b) 2 linear equations are independent
c) 2 linear equations are inconsistent
22. Graph the system of equations , then solve it algebraically .
23. Solve each system of equations:
24. Solve the system of equations.
25. Solve the system graphically.
26. A concert sold 884 tickets. Tickets cost $5 and $8. If
the total receipts were
$6,376, how many of each ticket were sold?
27. Find the domain and range of the relation:
. Also find the domain and range of the inverse of
28. If , find
29. Find the inverse of the function .
30. a) Write in exponential form.
b) Write in logarithmic form .
31. Write as a sum or difference of logarithms:
32. Write as a single logarithm with a coefficient of 1.
34. If , find x.
35. Graph each of the following functions:
36. Solve for x:
37. Find x if .
38. Solve for x.
19. The graph is a parabola .
21. a) The lines coincide. There are infinitely many
b) The lines intersect at one point.
c) The lines are parallel. There is no solution.